[Bored chemist]

Perhaps I can add another example. The air inside a running microwave oven, radio wave oven, induction cooker, laser oven, may show different temperature measurement value, depending on the thermometer type used.

Temperature is still only meaningful if a system is at equilibrium.

For some systems- far from equilibrium- the temperatures can be different- or even negative.

[hamdani yusuf (OP)]

Temperature is still only meaningful if a system is at equilibrium.

How do you define equilibrium?
Imagine a frozen pond in a winter. The depth is 10 meters. The air temperature above the surface is -10°C. One meter ice layer has been formed on the surface. The rest of the pond is still liquid water. This condition hasn't changed for a week. Is it in equilibrium?

[Bored chemist]

Temperature is still only meaningful if a system is at equilibrium.

How do you define equilibrium?
Imagine a frozen pond in a winter. The depth is 10 meters. The air temperature above the surface is -10°C. One meter ice layer has been formed on the surface. The rest of the pond is still liquid water. This condition hasn't changed for a week. Is it in equilibrium?

No. It can't be at eqm because it has a temperature gradient.
That's because heat is flowing from the Earth's core, into the water, up through the ice and out again.

[alancalverd]

The air inside a running microwave oven, radio wave oven, induction cooker, laser oven, may show different temperature measurement value, depending on the thermometer type used.

No. The temperature of the air (assuming it is well stirred and thus in internal equilibrium) has a unique value. The practical problem is that the power source interacts differently with different types of thermometer and if you aren't careful you end up measuring the microwave absorbtivity of a thermocouple or whatever, or even generating a load of sparks and no data. An external thermistor bolometer is probably the simplest practical device for an industrial oven but even then you need to ensure that the emissivity of the air is greater than that of the oven itself - quite difficult to do. If the oven is ventilated, you could put a glass bottle gas thermometer inside and measure the pressure of the working volume of air, which will be close to that of its ambient. If it isn't ventilated, than a pressure gauge will give you the answer. 

[alancalverd]

For some systems- far from equilibrium- the temperatures can be different- or even negative.

The concept of negative temperature is interesting but AFAIK it can never be more than a concept. Something to do with Carnot, but then you can't trust the French.

[Eternal Student]

Hi.

For objects that are not ideal gas, their temperature can be defined as the same as the ideal gas which don't exchange energy with them when they are in contact

   Yes.   That is one option and I'm sure it's the most common choice.   This is often called a thermodynamic approach to defining temperature.   Define two temperatures to be equivalent when heat doesn't flow from one body to the other when they are in thermal contact.
    It involves macroscopic properties of the two bodies or two systems and some issues deciding what criteria must be met to say the two systems are in thermal contact.  A lot of this has been discussed earlier.
    There are alternative ways to define the temperature of a system that isn't an ideal gas which still try to connect it to temperature of an ideal gas, like sticking a thermometer into the test system and also into some samples of ideal gas held at known temperatures.  Declare them to be at the same temperature if the thermometer reads the same.

    Extending the definition of temperature to objects that aren't ideal gases would involve a hybrid of approaches to defining temperature  (for example,  the ideal gas law for the ideal gas  +  Thermodynamic approach for the test object transferring heat to the ideal gas ;      or     ideal gas law for the ideal gas  +   empirical temperature definition with a thermometer).

     It's been said before but "temperature" is a difficult thing to define.
Wikipedia has a decent section describing various approaches for defining temperature which they describe as different "temperature scales" including:
Scales based on a thermodynamic approach;  Empirical Scales based on physical properties that a thermometer device can have; Theoretical scales such as that obtained by using kinetic theory;  Temperature scales just for an ideal gas obtained from the equation of state or ideal gas law.
See:   https://en.wikipedia.org/wiki/Temperature#Classification_of_scales

    There are few systems for which temperature, especially a definition based on kinetic theory of particles, is really well understood.  I would say ideal gases are the only object for which it is well understood (but this is a simplification.  The spirit of it is correct, kinetic theory and temperature for ideal gases is well understood and it isn't for much else.   There are some theoretical constructions like crystal lattices for which some kinetic theory has been studied and possibly some other things in the literature which I haven't had the time to look at).   Anyway, for an ideal gas, all the different definitions or approaches to determining temperature become identical.   
Specifically,
 1.  two samples of ideal gas have the same temperature      if and only if
 2.  there is no transfer heat from one system to the other when they are in thermal contact      if and only if     
 3.  their particles have the same average k.e.       if and only if
 4.  a thermometer stuck into each sample reads the same         if and only if     
 5.  some other measure of temperature that I might have accidentally forgotten gave the same result.   

   For objects that aren't ideal gases it's not clear that all the definitions or approaches for determining temperature would give the same results.
- - - - - - - - - -

Practical methods to measure temperature, such as used in mercury and alcohol thermometer, bimetal, thermocouple, RTD, and infrared thermometer are less reliable, involve non-linearity, and have narrower range and use case.

    Yes.   Although it's fairly arbitrary to say that these practical or thermometer based approaches to defining temperature show non-linearity.   It implies that some other measure of temperature like that based on kinetic theory is better or more truthful.   Perhaps the thermometer based approach is the right one and the absolute temperature that seems to have been standardized as the Kelvin scale shows non-linearity in comparison to that.
    Historically, thermometers and/or the ideal gas law were used to measure and define temperature when thermodynamics was being developed.  It wasn't until later that they realised it may not be measuring exactly what they wanted to measure for the most logical and streamlined formulation of thermodynamics and/or of microsocopic statistical mechanics.
- - - - - - - - - -

Perhaps I can add another example. The air inside a running microwave oven, radio wave oven, induction cooker, laser oven, may show different temperature measurement value, depending on the thermometer type used.

  Yes.   See earlier discussion.  Different thermometers and indeed different approaches to trying to define temperature can give different results for the temperature.
   As @Bored chemist  outlined:   You have to be careful what you try and assign a temperature to.   Is the air inside a running microwave just going to be considered as the air particles (like N₂ molecules) and the application of kinetic theory to the motion of those particles   OR   as a composite object which is the entire contents of the oven and consists of air particles + the photons in it.   If you were trying to determine the temperature of the composite object then the energy doesn't seem to have been equi-partioned yet:  There is far more radiation in the microwave range then there should be for the natural radiation properties of the air.   The contents of the oven isn't in a state of equilibrium yet.   Give it more time and a well defined temperature should appear, of course that won't happen while the oven is left switched on and running, you're putting microwaves into it faster than the natural processes in the air and perhaps also in the walls of the oven can re-distribute and equi-partition the energy.

---Stopped writing, this is already too long and has overlapped with other replies---

Best Wishes.

[Bored chemist]

For some systems- far from equilibrium- the temperatures can be different- or even negative.

The concept of negative temperature is interesting but AFAIK it can never be more than a concept.

The population inversion in a laser corresponds to a negative thermodynamic temperature.
It's a long way from equilibrium so a temperature isn't well defined. That's the point.

[Bored chemist]

No. The temperature of the air (assuming it is well stirred and thus in internal equilibrium) has a unique value.

No.
It's possible for the rotational temperature of the water vapour to be different from the translational temperature  or , especially if there's any ionisation, for the electron temperature to be different again.

[Bored chemist]

We know, by definition, the temperature of water at its triple point.
It isn't an ideal gas,

[Eternal Student]

Hi.

We know, by definition, the temperature of water at its triple point.
It isn't an ideal gas,

    That's a definition of one value for a temperature for one type of macroscopic system.  It doesn't provide a whole scale of temperature or any sense of how I can declare that another type of system (perhaps some liquid alcohol) is at the same temperature.
    It is often extended to a whole scale of temperature such as the Celsius system, where the boiling point of water is used as the other fixed point of the scale and a thermometer device like a mercury thermometer has the difference in the height of the mercury column divided into 100 units  (well it was 100 units when the freezing point of water was the lower fixed point, which is what they first used - but it's about 99.99 units if you use the triple point).   The usual way of applying the same definitions of temperature to other systems (things that aren't just water) is to just stick the thermometer into that other system and take a reading of the height of the mercury column.   Anyway, the whole system is then seen to be an empirical approach (it uses physical properties of a thermometer device) to define a temperature scale.

Best Wishes.

[Bored chemist]

That's a definition of one value for a temperature for one type of macroscopic system.  It doesn't provide a whole scale of temperature

It  (together with the definition of absolute zero) is the only fixed point on the whole of the Kelvin temperature scale.

Last time I checked, they compared things to the water point, using a constant volume helium thermometer extrapolated to zero pressure.
That is, in effect, using the ideal gas laws.

This might be helpful.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4865254/

[Eternal Student]

Hi.

This might be helpful.
https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4865254/

   That is interesting and I've only scanned through it so far.  I'll read more later.
   As far as I can see the latest revisions to the Kelvin temperature scale were made in 2019 and that paper or article was written in 2016.  I think they (the article referenced) are talking about the modifications that were about to bring the standard to what it is now.

    I think there's a mis-print in the article (first paragraph under the title Gas Thermometry) :

Gas thermometry relies on the statistical-mechanical connection between the three kinetic degrees of freedom of an ideal gas and thermodynamic temperature: ½ m〈v²〉 = 3k_BT, where m is the mass of an atom and 〈v²〉 is the mean-square velocity of the atom.

   I'm fairly sure  that should be   ½ m〈v²〉 = (3/2) . k_BT.

   Anyway, if you (@Hamdani) are really interested in the best way to define temperature it might be well worth having a look at that article and the simpler overview of the situation in Wikipedia.

It (the triple point of water) (together with the definition of absolute zero) is the only fixed point on the whole of the Kelvin temperature scale.

   The latest definition of the Kelvin scale for temperature won't require the triple point of water as a fixed point.
Since May 2019, that value (the triple point of water) has not been fixed by definition but is to be measured through microscopic phenomena

[Quote from Wikipedia]

    Even absolute zero,  0 K,  doesn't really fit the description of what we would have called a "fixed point" in the old days.  No experiment has to be done or object set up to that temperature to calibrate the scale.   That value just falls out naturally from the theoretical definition of temperature from statistical mechanics.  You also have no choice about what numerical value you assign to this temperature,  it couldn't be -10  or  +10 because it's got to be proportional to the average kinetic energy of particles (which is supposed to be nothing).   
    You don't really have any freedom to set any fixed points and corresponding numerical values at those fixed points for the temperature.   For example, if you use the equation   ½ m〈v²〉 = (3/2) . k_BT,  to define temperature, T,  then the only way you can adjust the value of T for some pre-determined reference situation (like the average k.e. of the gas particles in an equilibrium mixture of ice, liquid and gas water, i.e. water at its triple point)  would be by changing the Boltzman constant.
    If I've read the article @Bored chemist  presented correctly,  the exact value of the Boltzman constant wasn't going to be fixed until 2018 (2 years after the paper was printed).  With the new value fixed, the triple point of water would be close to 273.16 Kelvin but there was no expectation that it would be exactly that value.

- - - - - - -
   There we go...  . I had no idea the way we think about temperature has changed that much and this recently.
Thanks again for the article @Bored chemist .

Best Wishes.

[hamdani yusuf (OP)]

Temperature is still only meaningful if a system is at equilibrium.

How do you define equilibrium?
Imagine a frozen pond in a winter. The depth is 10 meters. The air temperature above the surface is -10°C. One meter ice layer has been formed on the surface. The rest of the pond is still liquid water. This condition hasn't changed for a week. Is it in equilibrium?

No. It can't be at eqm because it has a temperature gradient.
That's because heat is flowing from the Earth's core, into the water, up through the ice and out again.

If I put thermometers at the bottom, middle, and top of the pond, they would show certain values. Are they meaningless?

[hamdani yusuf (OP)]

The air inside a running microwave oven, radio wave oven, induction cooker, laser oven, may show different temperature measurement value, depending on the thermometer type used.

No. The temperature of the air (assuming it is well stirred and thus in internal equilibrium) has a unique value. The practical problem is that the power source interacts differently with different types of thermometer and if you aren't careful you end up measuring the microwave absorbtivity of a thermocouple or whatever, or even generating a load of sparks and no data. An external thermistor bolometer is probably the simplest practical device for an industrial oven but even then you need to ensure that the emissivity of the air is greater than that of the oven itself - quite difficult to do. If the oven is ventilated, you could put a glass bottle gas thermometer inside and measure the pressure of the working volume of air, which will be close to that of its ambient. If it isn't ventilated, than a pressure gauge will give you the answer. 

In a microwave oven, the thin metal in the bolometer can absorb the radiation and generate heat, which may exceed the air temperature inside the oven chamber.

[Bored chemist]

If I put thermometers at the bottom, middle, and top of the pond, they would show certain values. Are they meaningless?

No, but "the temperature of the pond" is meaningless.
It has more than one temperature. A lot will be near 4 C, some  will be between 4 and zero, some will be very near zero.

[alancalverd]

In a microwave oven, the thin metal in the bolometer can absorb the radiation and generate heat, which may exceed the air temperature inside the oven chamber.

Only a fool would put anything but a gas thermometer inside a microwave oven to measure the air temperature. Dry air would work pretty well, but argon is even closer to an ideal gas.

The bolometer trick is to use a concave mirror to focus the radiation from the air onto the thermistor, all from outside the oven.

The engineer who lives inside my head wants to ask why you are interested in the air temperature inside an oven. Most people are more interested in the wall temperature, which determines the thermal radiative heating of whatever you want to cook, or the power input to the microwave or fan heater.

[Bored chemist]

Only a fool would put anything but a gas thermometer inside a microwave oven to measure the air temperature.

Not really.
https://www.amazon.co.uk/Brannan-Microwave-Thermometer/dp/B005RDUSAW
Though it wouldn't achieve much to measure air temperature in a microwave.

Most people are more interested in the wall temperature,

Not if it's a microwave oven.

The engineer who lives inside my head wants to ask why you are interested in the air temperature inside an oven.

Because they know that the heat carried by that air in a conventional oven is a significant part of the cooking process.
That's why cooking times are reduced in fan ovens.

Most people are more interested in the wall temperature

I think more people are actually interested in how quickly stuff cooks.
That's related to wall temperature and air temperature in a conventional oven;  and related to the power density in a microwave oven.

[alancalverd]

Generally true for domestic cookers and bread ovens but I'm also thinking of things like pizza ovens, glassblowers furnaces, and the ovens they use to cook the paint on cars and dispose of corpses.

Bit of a sensitive point as, in a former incarnation, I was asked to review the draft European Directive on Physical Hazards which would have prevented the construction of any oven that could accommodate a human!

Not really.
https://www.amazon.co.uk/Brannan-Microwave-Thermometer/dp/B005RDUSAW

always read the small print:

This a Meat thermometer , has metal skewer , there are no instructions. and look on Makers site , No trace of this product?
Answer:The metal skewer is to make a hole in meat etc to enable the thermometer to be inserted more easily. You don't put the thermometer IN the microwave - you simply use it to check the temperature of the foods you have cooked in there.

Which is just as well. If it's an alcohol-in-glass instrument, it's quite likely to boil and shatter in a microwave, even if the ambient air is cold. And I wouldn't shove a glass thermometer into a lump of dead meat that I was going to eat - the rectum of a dog is dodgy enough! - so it's probably plastic, and likely to melt in the cooker even in the absence of air.

[Bored chemist]

always read the small print:

I did
http://taylor-enviro.com/media/IBs/514_ib.pdf
para 5

[Bored chemist]

Bit of a sensitive point as, in a former incarnation, I was asked to review the draft European Directive on Physical Hazards which would have prevented the construction of any oven that could accommodate a human

Bull?